Approximating a Sequence of Observations by a Simple Process
Dinah Rosenberg, Eilon Solan and Nicolas Vieille
Given a sequence s0,s1,…,sN of observations from a finite set S, we construct a process (sn) that satisfies the following properties:
(i) (sn) is a piecewise Markov chain with at most S pieces,
(ii) the conditional distribution of sn given s0,…, sn-1 is close to the empirical transition given by the observed sequence, for most n's, and
(iii) under (sn), with high probability the empirical frequency of the realized sequence is close to the one given by the observed sequence.
We generalize this result to the case that the conditional distribution of sn given s0,…, sn-1 is required to be in some polyhedron V(sn-1).
This result is used in the paper “Stochastic Games with Imperfect Monitoring”.